1. Field of the Invention
This invention relates to the study of ionic current due to membrane conductance changes in single cells. Much of the electrophysiology of cells--such as the generation of the action potential--is related to the flow of ionic current across the cell membrane in response to complex membrane conductance changes. To understand the electrophysiology of such cells, it is necessary measure this ionic current and characterize the membrane conductance changes.
2. Description of the Prior Art
The Voltage Clamp Amplifier
An apparatus know as a voltage clamp amplifier (VCA), in conjunction with a glass pipette electrode, is used to measure ionic current and conductance in single cells, as shown in FIG. 1A.
Referring to FIG. 1A, a VCA 5 generates a command voltage Vc 41, and is connected to a cellular microelectrode, patch electrode or pipette electrode 10, the fabrication of which is well known in the art. Pipette 10 is in electrical contact with a cell 15. FIG. 1B shows an equivalent circuit of pipette 10 and cell 15. As shown, pipette 10 has a pipette series resistance Rs, a pipette shunt capacitance Cp, a pipette voltage Vp, and a pipette current Ip. Thus pipette 10 is modeled by a single RC section formed by Rs and Cp. Cell 15 has a membrane resistance Rm, a membrane capacitance Cm, and a membrane voltage Vm.
The VCA acts as a low impedance voltage source, setting the pipette voltage Vp equal to the command voltage Vc 41. If Rs and Cp are small enough to be ignored, the cell membrane voltage Vm.congruent.Vp and Vc 41 is imposed across the cell membrane. Vm is then said to be "clamped" to Vc. Under these conditions, measuring the pipette current Ip provides a direct measure of the cellular ionic current. The cellular ionic conductance G can then be computed as: ##EQU1## The Effects of Series Resistance (Rs)
In practice, the main difficulty with this arrangement is that the large pipette series resistance Rs limits the voltage clamping bandwidth. The time constant that determines voltage clamping bandwidth is given by: EQU .sub..tau.vclamp =R.sub.s C.sub.m
A typical Rs, Cm combination of 5 Meg and 50 pF gives a time constant of 250 us, or a bandwidth of 637 Hz. While this is sufficient bandwidth to record slow ionic currents, rapid ionic currents--such as Na.sup.+ current that underlies the action potential in cardiac or neuronal cells--require a voltage clamping bandwidth of .about.10 kHz to be resolved. Therefore, in order to voltage clamp rapid ionic currents in single cells, it is necessary to compensate for the bandwidth-lowering effects of series resistance.
Rs Compensation
Three principal methods are in use to compensate for series resistance effects using a single electrode VCA: conventional Rs compensation, steady state Rs compensation, and compensation using discontinuous or pulsed feedback. Each method is only partially effective, so that voltage clamping rapid ionic current using these methods--especially in large cells where the membrane capacitance Cm is large--is extremely difficult.
Conventional Rs Compensation
Conventional Rs compensation is widely used to increase the recording bandwidth of the single electrode VCA (see Electronic Design of the Patch Clamp by F. J. Sigworth, 1983, found in Single-Channel Recording, edited by B. Sakmann and E. Neher, p. 29-32.). As shown in FIG. 2, conventional Rs compensations uses a feedback circuit to add an Rs correction signal Rscorr 30 to the command voltage Vc. Rscorr 30 is computed as a scaled value of the measured pipette current Ipmeas 75, where Ipmeas 75 comes from pipette current measurement means 74. Rscorr 30 is given by: EQU Rscorr=I.sub.pmeas R.sub.s .alpha.
where .alpha. is a scaling constant ranging from 0 (no Rs compensation) to 1 (100% Rs compensation). Ideally, when .alpha..fwdarw.1 the membrane voltage Vm follows the command voltage Vc exactly, independently of Rs. In practice, conventional Rs compensation is unstable at high compensation settings. Sigworth's analysis traces the main cause of this instability to stray capacitance effects of the pipette electrode: conventional Rs compensation as shown in FIG. 2 assumes pipette 5 behaves like a pure resistance Rs, whereas a real pipette electrode has stray shunt capacitance Cp (as shown previously in FIG. 1B). Pipette current shunted through this stray capacitance introduces an erroneous correction signal that destabilizes the Rs compensation feedback loop. To improve stability it is necessary to neutralize this stray pipette capacitance electronically using a positive feedback network. This capacitance neutralization circuitry is itself prone to instability (see Guld, C. 1962. Cathode follower and negative capacitance as high input impedance circuits, Proc. IRE. 50:1912-1927). Consequently, even when using maximum capacitance neutralization .alpha. is limited to .about.0.8, corresponding to 80% series resistance compensation. This is usually insufficient to voltage clamp fast ionic current. In addition, slight shifts in Rs or Cp--as happens when the pipette immersion depth changes--easily drives conventional Rs compensation circuitry from a marginally stable state into oscillation, killing the cell under study.
Steady State Rs Compensation
Moore et. al. (Moore, J. W., M Hines, and E. M. Harris. 1984. Compensation for resistance in series with excitable membranes. Biophys. J. 46:507-514) and Strickholm (Strickholm, A. 1995. A single electrode voltage, current and patch-clamp amplifier with complete stable series resistance compensation. J Neurosci. Methods. 61:53-66.) each describe similar modifications to conventional Rs compensation that feed back a scaled value of the steady state pipette current as opposed the total pipette current. In steady state Rs compensation, Rscorr 30 is given by: EQU Rscorr =I.sub.steady-state R.sub.s .alpha.
where I.sub.steady-state is computed using an electronic bridge circuit that subtracts the membrane capacitive current from the measured pipette current Ipmeas 75. Steady state Rs compensation is not destabilized by stray pipette capacitance--as is the case with conventional Rs compensation--and 100% compensation values can be used. By subtracting the membrane capacitive current, there is effectively no Rs compensation when the command potential Vc changes. Consequently, to increase the rate of membrane charging when Vc is changed, Strickholm outlines the use of a supercharging potential that is added to Vc. (see Strickholm, A. 1995. A supercharger for single electrode voltage and current clamping. J Neurosci. Methods. 61:47-52).
Limitations of Steady State Rs Compensation
A serious limitation with steady state Rs compensation occurs when the system is used with a single electrode VCA to voltage clamp large, rapidly activating ionic currents such as Na.sup.+ current in single cells. This limitation is due to the fact that the electronic bridge assumes a fixed value for the membrane resistance Rm in order to compute and subtract off the membrane capacitive current. When large ionic currents are voltage clamped, Rm can change by factors of 100 or more and unbalance the electronic bridge. When this happens the voltage clamp recovery time can be &gt;1 ms, which is too slow to maintain voltage clamp control of rapid ionic currents. This situation is shown in FIG. 3. FIG. 3 plots the membrane voltage Vm using steady state Rs compensation. Initially Rs=5 Meg, Rm=100 Meg, and Cm=50 pF--typical values for a pipette electrode and cell--and the electronic bridge is balanced for these values. At t0 the command voltage undergoes a stepwise transition from 0 to 100 mV. After .about.1 ms the membrane voltage charges to the command voltage of 100 mV. At tl Rm makes a stepwise transition from 100 Meg to 20 Meg, simulating a rapid, large ionic conductance change. As shown, the membrane voltage Vm escapes from the clamping voltage of 100 mV at t1, and takes until t2 before Vm is again clamped at 100 mV. It should be noted that using the supercharging procedure described by Strickholm will increase the initial rate of membrane charging when Vc is changed at t0, but will not affect in any way the slow voltage clamp recovery time exhibited when Rm changes at t1.
Discontinuous Feedback Amplifiers
Another approach to combat series resistance effects is originally described by Brennecke et. al. (Brennecke, R. and B. Lindemann. 1972. Theory of a membrane voltage clamp with discontinuous feedback through a pulse current clamp. Rev. Sci. Instrum. 45:184-188) and implemented by Wilson et. al. (Wilson, W. A, Goldner 1975. Voltage clamping with a single microelectrode. J Neurobiol. 6:411-22). Variously called switch-clamp, pulsed current clamp or discontinuous feedback voltage clamp amplifiers, these designs operate on the principle of repetitively cycling between current passing and voltage measuring modes. During voltage measuring mode, the membrane voltage is measured and stored while no current is passed down the electrode. During current passing mode, the stored membrane voltage is compared with the command voltage and used to determine a current injection pulse. This current injection pulse acts as negative feedback to keep the membrane voltage clamped at the command voltage Vc. Since the membrane voltage is measured while no current is being passed down the electrode, there is no voltage drop across Rs, and hence the speed of the clamp becomes independent of Rs. The attainable bandwidth is limited by the maximum switching rate used. Finkel et. al. (Finkel, A. S. and S. J. Redman. 1984. Theory and operation of a single microelectrode voltage clamp. J. Neurosci. Methods. 11:101-127) show that the maximum stable switching rate is limited by the stray pipette capacitance Cp. Consequently, in order to increase the switching rate, it is necessary to neutralize the pipette capacitance electronically, as with conventional Rs compensation. This capacitance neutralization compromises the stability of the voltage clamp. The attainable voltage clamp bandwidth using discontinuous feedback is generally insufficient to resolve rapid Na.sup.+ currents.
Modified Swtich-Clamp Amplifiers
Steffin obtained U.S. Pat. No. 4,441,507 (1984) by applying modifications to switch clamp designs to improve bandwidth. His patent outlines a high frequency equalization network on the input stage, as well as low frequency and transient compensation networks. His switch clamp also employs electronic capacitance neutralization circuits as with existing designs. Consequently, obtaining rapid switching rates is dependent on finely tuning capacitance neutralization circuitry, as well as tuning the aforementioned equalization and compensation networks. This makes for an unstable voltage clamp that cannot tolerate parameter changes. Slight changes in pipette stray capacitance will lead to unstable operation, as with conventional Rs compensation.
The Twin Electrode Voltage Clamp
A very successful approach to combat series resistance effects is based on using two pipette electrodes instead of one. A twin electrode voltage clamp uses one electrode to measure Vm; the other electrode is used to pass current to clamp the membrane voltage at Vc in a negative feedback loop. Referring to FIG. 4, command voltage 41 is compared to a feedback signal 65. Feedback signal 65 is generated by buffer amplifier 60, which buffers the membrane voltage Vm measured by pipette 35. The result of this voltage comparison forms an error voltage signal 40. The error signal 40 is subject to a feedback controller 45 and a controlled current source 55, the fabrication of which are well known in the art. Controller 45 takes as input error voltage signal 40 and outputs control voltage 50. Current source 55 takes as input control voltage 50 and outputs the pipette current Ip, where Ip is made proportional to the input control voltage 50 by the action of current source 55. The output of current source 55 into pipette 5 and cell 10 acts as negative feedback to clamp the cell membrane potential Vm to the command potential Vc.
With the twin electrode configuration, the series resistance Rs is contained within the feedback loop and hence does not limit the voltage clamping bandwidth.
While the twin electrode configuration creates a wide bandwidth voltage clamp, it is generally unsuitable for use with single cells, owing to the difficulty of impaling two electrodes in single cell. Consequently, to voltage clamp rapid ionic current in single cells requires using a single electrode VCA and compensating for series resistance Rs in some manner.
In summary, the methods of series resistance compensation for a single electrode VCA hithertofore in use all suffer from a number of disadvantages:
a. As they increase bandwidth, there is a corresponding decrease in stability. This makes them extremely difficult to use. PA1 b. Most require the careful use of pipette capacitance neutralization, which further reduces stability. PA1 c. Stable variants assume a fixed membrane conductance, making them too slow to resolve rapid ionic currents. PA1 a. to provide full, stable series resistance compensation for a single electrode voltage clamp without the need to null stray capacitance electronically; PA1 b. to provide series resistance compensation for a single electrode voltage clamp that is independent of cell conductance changes, so that large, fast ionic currents can be voltage clamped; and PA1 c. to provide series resistance compensation for a single electrode voltage clamp that has wide stability margins, ensuring stable operation even as parameters change during an experiment.